If x ft of stonewall is used as one side of the field expres

If x ft. of stonewall is used as one side of the field, express the area enclosed as a function of x according to the problem below.

A farmer has 600ft of woven wire fencing available to enclose a rectangular field and to divide it into three parts by two fences parallel to one end.

If x ft. of stonewall is used as one side of the field, express the area enclosed as a function of x when the dividing fences are parallel to the stone wall.

Solution

Since the field is rectangular, we\'ll establish the dimensions length and width as x and y.

Now, we know, from enunciation that there are available 600 ft wire to enclose the field and to build more wire walls, namely 2 inner walls, parallel to the stone wall.

So, the total amount of 600 ft could be expressed as:

3x + 2y = 600 (1)

We did not put 4x because one wall is made of stone and we did not put 2x because we have 2 more inner wire walls, besides the end wall.

To calculate y with respect to x, we\'ll subtract 3x both sides, in (1).

2y = 600 - 3x

We\'ll divide by 2:

y = 300 - 3x/2 (2)

Now, we\'ll express the area enclosed:

A = length*width

A = x*y

We\'ll substitute y by (2):

A = x*(300 - 3x/2)

We\'ll remove the brackets and we\'ll have:

A = -3x^2/2 + 300x